The Jan. 1858 issue of the Chess Monthly (p.30) gives a total score in New York of Morphy against Thompson as +8-0=0. Taking out +3-0=0 for their tournament games leaves +5-0=0 from offhand games, as also given by Sergeant. These games must have been played between Morphy's arrival in New York on 5 Oct. 1857 and 16 Nov. 1857, the date of a letter by Morphy (given by Lawson and Sarah's Morphy website) giving the +8-0=0 total. According to Lawson, the first of these was played on 8 Oct. 1857.